Landau fragmentation and deformation effects in dipoSe response of sodium clusters

Recent experimental data on the dipole plasmon in axial sodium clusters Na _N ⁺ with 11 ≤ N ≤ 57 are analyzed within a self-consistent separable random-phase approximation (SRPA) based on the deformed Konh-Sham functional. Good agreement with the data is achieved. The calculations show that, while in light clusters plasmon properties (gross structure and width) are determined mainly by deformation splitting, in medium clusters with N τ 50 the Landau fragmentation becomes decisive. Moreover, in medium clusters shape isomers come to play with contributions to the plasmon comparable with the ground state one. As a result, commonly used methods of the experimental analysis of cluster deformation become useless and correct treatment of cluster shape requires microscopic calculations.     

Geometrical and quantal fragmentation of optical response in

By comparing quantal and semi-classical calculations of optical response, we work out the part of the splitting of the plasmon spectra which is exclusively due to geometrical effects. We apply the analysis to the test case which exhibits an interesting geometry with strong prolate quadrupole deformation and a pronounced asymmetry in addition. We find a new type of resonance splitting which is due to geometrical effects but goes beyond the simple and well known deformation splitting. Received: 6 April 1998 / Accepted: 24 April 1998     

Stability and fragmentation of multiply ionized clusters

The stability of neutral, singly and multiply ionized silicon clusters, (N = 2-7, M = 0, , , ), has been investigated using an ab initio density functional method. We show that the fragmentation effect significantly affects the structure of mass-spectra of multiply ionized silicon clusters. For clusters, the clusters with a large fragmentation energy are found to correspond to the high peaks at N = 4 and 6 in mass-spectra. For clusters, a peak at N = 5 in mass-spectra has been predicted to be especially high. Received: 9 June 1997 / Revised: 8 January 1998 / Accepted: 25 February 1998     

Electronic structure and magnetism in 4d-transition metal clusters

We analyze the stability of magnetic states obtained within the tight-binding model for cubooctahedral (O_h) and icosahedral (I_h) clusters of early 4d (Y, Zr, Nb, Mo, and Tc) transition metals. Several metastable magnetic clusters are identified which suggests the existence of multiple magnetic solutions in realistic systems. A bulk-like parabolic behavior is observed for the binding energy of O_h and I_h clusters as a function of the atomic number along the 4 d-series. The charge transfer on the central atom changes sign, while the average magnetic moments present an oscillatory behavior as a function of the number of d electrons in the cluster. Our results are in agreement with other theoretical calculations. Received: 20 November 1997 / Received in final form: 9 March 1998 / Accepted: 30 March 1998     

Charge transfer between alkali cluster ions and atoms in the 1 to 10 keV collisional energy range

The cross-sections for collisional charge transfer between singly charged free clusters M _n ⁺ (M = Li, Na; n=1...50) and atomic targets A (cesium, potassium) have been measured as a function of collisional relative velocity in laboratory energy range 1–10 keV. For each cluster size, the experimental values of the charge transfer cross-section are fitted with an universal parametric curve with two independent parameters and v_m, the maximum cross-section and the corresponding velocity. For small size clusters (), the characteristic parameters show strong variations with the number of atoms in the cluster. Abrupt dips observed for n=10 and n=22 are attributed to electronic properties. Charge transfer patterns observed for various collisional systems present similarities, which appear more sensitive to cluster quantum size effects than to collision energy defects. In their whole, the and v_m parameters show differences in both their size evolution and their absolute values discussed in term of projectile and target electronic structures. Received 13 April 2000 and Received in final form 29 June 2000     

Towards spectral pattern of spin polarized sodium clusters: The example of Na

We investigate spin modes in the ground state and the polarized first isomer of the Na₁₂ cluster describing the valence electrons in time-dependent local-spin-density approximation (TDLSDA) and the detailed ionic background using local pseudopotentials. The spin modes show a collective redshift compared to the unperturbed particle-hole excitations. They are strongly fragmented and the average energy of the modes along the principal axes are related to the underlying geometry (triaxial or axially symmetric). For the polarized isomer, we find significant cross talk between the spin modes and the dipole plasmon, which hints at a possible spectroscopic identification. Received: 22 June 1998 / Accepted: 29 July 1998     

Predictions of geometrical structures and ionization potentials for small barium clusters Ba

The geometrical structure of ground state Ba_n clusters (n =2-14) has been predicted from various types of calculations including two ab initio approaches used for the smaller sizes namely HF+MP2( n =2-6), DFT (LSDA)( n =2-6, 9) and one model approach HF+pairwise dispersion used for all sizes investigated here. The lowest energy configurations as well as some isomers have been investigated. The sizes n =4, 7 and 13 are predicted to be the relatively more stable ones and they correspond to the three compact structures: the tetrahedron, the pentagonal bipyramid and the icosahedron. The growth behavior from Ba₇ to Ba₁₃ appears to be characterized by the addition of atoms around a pentagonal bipyramid leading to the icosahedral structure of Ba₁₃ which is consistent with the observed size-distribution of barium clusters. Values for vertical ionization potentials calculated for n =2-5 at the CI level are seen to be in quite good agreement with recent measures. Received: 14 May 1997 / Received in final form: 2 February 1998 / Accepted: 27 February 1998     

Photodissociation dynamics of Cl in a xenon cluster

The photodissociation of a chlorine molecule in the environment of a xenon cluster has been studied experimentally using the real time pump and probe technique through the formation of an XeCl reaction product. The photodissociating system is probed in such a way that the movement of a single chlorine atom in the xenon environment is detected. Various Xe_nCl₂ cluster sizes have been investigated leading to the distinction between uncapped, half-capped and doubly capped structures for these clusters. These structures have a profound influence on the photodissociation dynamics. Retrapping of one chlorine atomic fragment and stabilization of the XeCl reaction product is only observed for the half and doubly capped clusters. The experimental work is complemented by classical molecular dynamics calculations to get a full picture of the photodissociation. Received: 17 February 1998 / Received in final form and Accepted: 28 July 1998     

Intracluster electron transfer from a metal atom/cluster followed by anionic oligomerization of vinyl molecules

Intracluster electron transfer and oligomerization reaction were investigated by mass spectrometry of clusters of alkali metal atom (M) with acrylonitrile (AN; CH₂=CHCN). In the photoionization mass spectra of M(AN)_n, magic numbers were clearly observed at n = 3k (k = 1-4 for M = Na and K, k = 1 for M = Li). The results of photodissociation of neutral K(AN)_n indicate that the n = 3 cluster has an anomalous stability relative to other sizes of clusters. The C=C bond in vinyl molecules is also found to be necessary to form the magic numbers by measuring the photoionization mass spectrum of K atom with propionitrile. These results strongly support the intracluster anionic oligomerization reaction initiated by electron transfer from the alkali atom. The quantum chemical calculations have revealed that the evaporation induced by excess energy generated by intracluster oligomerization is important to form the magic numbers in the present clusters. Received 29 November 2000     

Ground-state geometries and stability of NaMg clusters using ab initio molecular dynamics method

The ground-state geometries, energetics and the stability of ( n =1-12) clusters are studied using ab initio molecular dynamics method. Our results indicate that the ground-state geometries of large clusters () are different from those of clusters where a trivalent impurity Al is added to the same monovalent host Na. Other features observed are an early appearance of 3-dimensional structure and a pentagonal growth path from n =6 up to n =11. As expected, the ground-state geometry of is not an icosahedron but can be viewed as a distorted form of one of the low lying geometries of cluster. In the energetically favored structures impurity atom Mg is never located at the center of the cluster. The stability analysis based on the energetics shows (8 valence electrons) to be the most stable. In addition there is a remarkable even-odd pattern observed in the dissociation energy and the second difference in energy which is absent in earlier studies of and clusters. Received: 16 September 1998 / Received in final form: 15 February 1999     

Optical properties of mixed clusters: comparative study of Ni/Ag and Pt/Ag clusters

The optical properties of mixed (Ni_0.5Ag_0.5)_n and Pt/Ag clusters are investigated in the size range 2-5 nm. Low Energy Ion Spectroscopy (LEIS) experiments show that the cluster surface is entirely covered by silver atoms for the two systems. The optical spectra of Ni/Ag clusters exhibit a large Surface Plasmon Resonance (SPR), damped and widened when the cluster size decreases, in agreement with a classical model assuming a core-shell geometry and including the reduction of the conduction electron mean-free path in the silver shell. For Pt/Ag clusters, no SPR emerges in the size range 2-5 nm, although it is predicted within a classical model, a pronounced SPR appearing only for clusters larger than 10 nm in diameter.     

Magnetic properties of small Yttrium clusters

The magnetic properties of small Y_N clusters are studied by using a tight-binding Hubbard Hamiltonian in the unrestricted Hartree-Fock approximation. Several types of cluster geometries are considered in order to see the effects of the size and symmetry of the structures on the magnetic properties. The average magnetic moments are found to be constant over large domains of variations in the interatomic distance, a fact that can be explained by the existing closed shell electronic configurations at least for one spin direction in all our magnetic solutions. Small energy gains upon the onset of magnetization are obtained, which reveals the low stability of the magnetic solutions. Our results contradict the prediction of a magnetic-nonmagnetic transition at a large cluster size (about 90 atoms) for these kinds of systems. Received: 27 April 1998 / Received in final form: 23 June 1998 / Accepted: 17 July 1998     

Photoionization of argon, krypton and xenon clusters in the inner valence shell region

Photoionization of rare gas clusters in the innervalence shell region has been investigated using threshold photoelectron and photoion spectrometers and synchrotron radiation. Two classes of states are found to play an important role: (A) valence states, correlated to dissociation limits involving an ion with a hole in its innervalence ns shell, (B) Rydberg states correlated to dissociation limits involving an ion with a hole in its outervalence np shell plus an excited neutral atom. In dimers, class A states are “bright”, that is, accessible by photoionization, and serve as an entrance step to form the class B “dark” states; this character fades as the size of the cluster increases. In the dimer, the “Mulliken” valence state is found to present a shallow potential well housing a few vibrational levels; it is predissociated by the class B Rydberg states. During the predissociation a remarkable energy transfer process is observed from the excited ion that loses its innershell electron to its neutral partner. Received: 10 February 1998 / Revised: 17 July 1998 / Accepted: 31 July 1998     

Local environment and electron correlation effects on the magnetic properties of clusters

The electronic and magnetic properties of clusters are investigated in the framework of the Hubbard model by treating electron correlations effects in a saddle-point slave-boson approximation. The size dependent single-particle spectrum is calculated using a third moment real-space expansion of the local density of states. Results for the magnetic moments, magnetic order, average number of double occupations and hopping renormalizations are given as a function of the local coordination number z, for different representative values of the Coulomb interaction strength U/t and band filling n. Several transitions between paramagnetic, ferromagnetic and antiferromagnetic behaviors are obtained as a function of z. The environment dependence of the magnetic behavior and of the degree of electron delocalization is analyzed. Advantages and limitations of the present approach are discussed. Received: 8 January 1998 / Revised: 22 June 1998 / Accepted: 6 August 1998     

Optical properties of gold metal clusters: A time-dependent local-density-approximation investigation

The optical response of free and matrix-embedded gold metal clusters Au_N is investigated in the framework of the time-dependent local-density-approximation (TDLDA). The characteristics of the surface plasmon resonance are carefully analyzed as a function of the model parameters and the particle radius. The strong influence of the frequency-dependence of the 5d core-electron dielectric function in the vicinity of the interband threshold is emphasized. The size evolution of the Mie-frequency in free gold clusters exhibits a noticeable blue-shift trend as the particle size decreases, much stronger than in silver clusters. The width and shape of the resonance, essentially ruled by the decay via the interband transitions, are found closely correlated to the imaginary component of the core-electron dielectric function. In presence of a surrounding matrix the blue-shift trend is largely rubbed out. Agreement with recent experimental results on size-selected gold clusters embedded in an alumina matrix may be achieved by taking into account the porosity effects at the metal/matrix interface. The comparison with the predictions of classical models is also provided. Received: 9 March 1998 / Revised: 5 June 1998 / Accepted: 3 July 1998     

Photoionization thresholds and structures of third group metals clustered with ammonia

A photoionization study of the Me(NH₃) clusters formed in the reaction of photoablated third group metal vapor with gaseous ammonia is reported. The photoionization spectra exhibit some features due to vibrational excitation of ionic clusters and to transitions to neutral Rydberg states leading to autoionization. DFT quantum chemical calculations are performed on the Me(NH₃). The cluster geometries are fully optimized imposing the C_3v symmetry. The calculated values of the IPs are in agreement with those experimentally determined. Received: 16 February 1998 / Revised and Accepted: 7 May 1998     

Dynamics of cluster deposition on Ar surface

Using a combined quantum mechanical/classical method, we study the dynamics of deposition of small Na clusters on Ar(001) surface. We work out basic mechanisms by systematic variation of substrate activity, impact energy, cluster orientations, cluster sizes, and charges. The soft Ar material is found to serve as an extremely efficient shock absorber which provides cluster capture in a broad range of impact energies. Reflection is only observed in combination with destruction of the substrate. The kinetic energy of the impinging cluster is rapidly transfered at first impact. The distribution of the collision energy over the substrate proceeds very fast with velocity of sound. The full thermalization of ionic and atomic energies goes at a much slower pace with times of several ps. Charged clusters are found to have a much stronger interface interaction and thus get in significantly closer contact with the surface.     

Ionic recoil energies in the Coulomb explosion of metal clusters

The photoionization of metal clusters in intense femtosecond laser fields has been studied. In contrast to an experiment on atoms, the interaction in this case leads to a very efficient and high charging of the particle where tens of electrons per atom are ejected from the cluster. The recoil energy distribution of the atomic fragment ions was measured which in the case of lead clusters exceeds 180 keV. Enhanced charging efficiency which we observed earlier for specific pulse conditions is not reflected in the recoil energy spectra. Both the average and the maximum energies decrease with increasing laser pulse width. This is in good agreement with molecular dynamics calculations. Received 20 December 2000